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1. Introduction
The global ocean circulation is of great importance for the earth’s climate system through its heat transport and the cycling and storage of carbon. Understanding the underlying physical processes that drive the global ocean circulation is essential for our understanding of the earth’s climate system and our ability to model it accurately. However, observing and modeling the global ocean circulation remains a challenge.
A component of the ocean circulation is buoyantly or density-driven due to thermohaline forcing and is often referred to as thermohaline circulation. Here, thermohaline forcing refers to boundary freshwater and heat fluxes and salt and heat fluxes by diffusive mixing. In this paper, we develop a description of the thermohaline circulation using its unambiguous relationship to the thermohaline forcing. The use of thermodynamic coordinates for understanding the relationship between the circulation and thermodynamic forcing was first made clear by Walin (1982). He showed that the area-integrated surface heat flux between two outcropping isotherms could be used to calculate the diathermal advection in a steady-state ocean.
Speer and Tziperman (1992) applied Walin’s framework to isopycnals instead of isotherms, which together with many subsequent studies (Marshall 1997; Marshall et al. 1999; Nurser et al. 1999; Sloyan and Rintoul 2000, 2001; Iudicone et al. 2008; Badin and Williams 2010; Nikurashin and Ferrari 2013) allowed an understanding of ocean circulation driven by thermohaline forcing. Using this framework, Nurser and Marsh (1998) showed that the total diapycnal transport can be expressed as a sum of a streamfunction difference and nonsteady component. The diapycnal transport can be fully expressed as a streamfunction only when the nonsteady component is small.
Streamfunctions have been widely used as a diagnostic to study ocean circulation. The advantage of scalar streamfunctions lies in their ability to represent the complex three-dimensional and time-varying ocean circulation in two dimensions, allowing new insight into the ocean circulation. A classic example is perhaps the meridional overturning streamfunction Ψλz, representing the zonally averaged ocean circulation in latitude λ and depth z coordinates. Because ocean currents tend to follow isopycnal surfaces rather than surfaces of constant depth, Döös and Webb (1994) calculated a streamfunction in latitude and potential density σ coordinates Ψλσ. They identified circulation cells related to the Atlantic overturning, the subtropical...